The Final moment at the end A, in a beam AB due to rotations θA, θB and downward settlement of support at B is given by:
1
\({{\rm{M}}_{{\rm{AB}}}} = {{\rm{M}}_{{\rm{FAB}}}} + \frac{{2{\rm{EI}}}}{{\rm{l}}}\left[ {2{{\rm{\theta }}_{\rm{A}}} + {{\rm{\theta }}_{\rm{B}}} - \frac{{3{\rm{\delta }}}}{{\rm{L}}}} \right]\)
2
\({{\rm{M}}_{{\rm{AB}}}} = {{\rm{M}}_{{\rm{FAB}}}} - \frac{{2{\rm{EI}}}}{{\rm{l}}}\left[ {2{{\rm{\theta }}_{\rm{A}}} + {{\rm{\theta }}_{\rm{B}}} - \frac{{3{\rm{\delta }}}}{{\rm{L}}}} \right]\)
3
\({{\rm{M}}_{{\rm{AB}}}} = {{\rm{M}}_{{\rm{FAB}}}} + \frac{{4{\rm{EI}}}}{{\rm{l}}}\left[ {2{{\rm{\theta }}_{\rm{A}}} + {{\rm{\theta }}_{\rm{B}}} - \frac{{3{\rm{\delta }}}}{{\rm{L}}}} \right]\)
4
\({{\rm{M}}_{{\rm{AB}}}} = {{\rm{M}}_{{\rm{FAB}}}} + \frac{{2{\rm{EI}}}}{{\rm{l}}}\left[ {{{\rm{\theta }}_{\rm{A}}} + 2{{\rm{\theta }}_{\rm{B}}} - \frac{{3{\rm{\delta }}}}{{\rm{L}}}} \right]\)